## Heisenberg’s Uncertainty Principle

Heisenberg’s uncertainty principle states that: ** If the x-component of the momentum of a particle is measured with an uncertainty ∆p_{x}, then its x-position cannot, at the same time, be measured more accurately than ∆x = ℏ/(2∆p_{x}).** The three-dimensional form of the uncertainty relations for position and momentum can be written as follows:

This principle indicates that, although it is possible to measure the momentum or position of a particle accurately. But it is not possible to measure these two observables ** simultaneously** to an

**accuracy. That is, we cannot localize a microscopic particle without giving to it a rather large momentum.**

*arbitrary*To understand this, consider measuring the position of a macroscopic object (you can consider a car) and the position of a microscopic system (you can consider an electron in an atom). On the one hand, to locate the position of a macroscopic object, you need simply to observe it; the light that strikes it and gets reflect back to the detector (your eyes or a measuring device). It can in no measurable way affect the motion of the object.

On the other hand, to measure the position of an electron in an atom, you must use radiation of very short wavelength (the size of the atom). The energy of this radiation is high enough to change tremendously the momentum of the electron; the mere observation of the electron affects its motion so much that it can knock it entirely out of its orbit.

It is therefore impossible to determine the position and the momentum simultaneously to arbitrary accuracy. For localized particle, its wave function would become zero everywhere else. And its wave would then have a very short wavelength. Also according to de Broglie’s relation *p *= **ℏ** /λ.

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